Finite Group Databasebeta

← C61×#33556 #29536989

Subgroups — C61×#33556 #29536989

Order 15616.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3540C211yesmaximal, characteristic, complemented
2C61×#3028C211yesmaximal, characteristic, complemented
3C61×#3025C211yesmaximal, characteristic, complemented
4C61×#3021C211yesmaximal, characteristic, complemented
5C61×#2200C214yesmaximal, complemented
6C61×#2198C214yesmaximal, complemented
7C61×#2128C211yesmaximal, characteristic, complemented
8C61×#2123C211yesmaximal, characteristic, complemented
9C61×#2120C211yesmaximal, characteristic, complemented
10C61×#585C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C61—21no—
12C61×H(3,𝔽4)—21no—
13C61×#560C2212yescomplemented
14C61×#559C2212yescomplemented
15C61×#556—21no—
16C61×#555—21no—
17C61×#551—21no—
18C61×#548—21no—
19C61×#546—21no—
20C61×#542—22no—
21C61×#542—21no—
22C61×#538—22no—
23C61×#536—21no—
24C61×#536C2211yescharacteristic
25C61×#535C2211yescharacteristic
26C61×#525—21no—
27C61×#525—21no—
28C61×#525C2211yescharacteristic
29C61×#458—21no—
30C61×#458—22no—
31C61×#458C2212yescomplemented
32C61×#458C2214yescomplemented
33C61×B(4,𝔽2)—21no—
34C61×B(4,𝔽2)C2212yescomplemented
35C61×#454—22no—
36C61×#453C2214yes—
37C61×#421—21no—
38C61×#413C2211yescharacteristic
39C61×#410—21no—
40C61×#410—21no—
41C61×#410C2211yescharacteristic
42C61×#410C2211yescharacteristic
43C61×#353C2214yescomplemented
44C61×#352C2212yescomplemented
45C61×#352C2214yescomplemented
46C61×AΣL(1,𝔽16)C2212yescomplemented
472−1+4×C61—21no—
482−1+4×C61—41no—
49H(5,𝔽2)×C61—21no—
50H(5,𝔽2)×C61—21no—
51H(5,𝔽2)×C61—41no—
52H(5,𝔽2)×C61C2312yes—
53C2×#41×C61—21no—
54C2×#41×C61—21no—
55C2×#41×C61—21no—
56C2×#41×C61—21no—
57C2×#41×C61—42no—
58C2×#41×C61C2311yescharacteristic
59C22×Q8×C61D411yescharacteristic, complemented
60C22×D4×C61D411yescharacteristic, complemented
61C23×C4×C61D411yescharacteristic
62AGL(1,ℤ/8)×C61—24no—
63AGL(1,ℤ/8)×C61—42no—
64C2×SD16×C61—41no—
65C2×D8×C61—41no—
66C2×M16×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61—21no—
69C4⋊Q8×C61—41no—
70#127×C61C2312yes—
71#126×C61—22no—
72#126×C61—22no—
73#126×C61—22no—
74#124×C61—22no—
75#124×C61—21no—
76#124×C61—22no—
77#124×C61—22no—
78#124×C61—21no—
79#124×C61—22no—
80#124×C61—22no—
81#124×C61—41no—
82#124×C61D412yescomplemented
83#123×C61—22no—
84#123×C61—22no—
85#123×C61—22no—
86#123×C61—24no—
87#123×C61—22no—
88#123×C61D411yescharacteristic
89#123×C61D412yescomplemented
90#123×C61C2312yes—
91#123×C61C2311yescharacteristic
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61—22no—
94C22⋊Q8×C61—21no—
95C22⋊Q8×C61—21no—
96C22⋊Q8×C61—21no—
97C22⋊Q8×C61—21no—
98C22⋊Q8×C61—42no—
99C22⋊Q8×C61—41no—
100#121×C61—21no—
101#121×C61—21no—
102#121×C61—22no—
103#121×C61—21no—
104#121×C61—21no—
105#121×C61—22no—
106#121×C61—22no—
107#121×C61—41no—
108#120×C61—22no—
109#120×C61—22no—
110#120×C61—21no—
111#120×C61—21no—
112#120×C61—22no—
113#120×C61D411yescharacteristic
114#120×C61C2311yescharacteristic
115C4×Q8×C61—21no—
116C4×Q8×C61—22no—
117C4×D4×C61—22no—
118C4×D4×C61—21no—
119C4×D4×C61—22no—
120C4×D4×C61—21no—
121C4×D4×C61—21no—
122C4×D4×C61—22no—
123C4×D4×C61—42no—
124#117×C61—22no—
125#117×C61—21no—
126#117×C61—21no—
127#117×C61—21no—
128#117×C61D411yescharacteristic
129#117×C61D411yescharacteristic, complemented
130#117×C61D411yescharacteristic, complemented
131C2×C22⋊C4×C61—22no—
132#104×C61—24no—
133#101×C61—21no—
134#100×C61C2312yes—
135#99×C61—21no—
136#99×C61—21no—
137#99×C61—22no—
138#99×C61—22no—
139#99×C61—24no—
140#99×C61C2312yes—
141#99×C61C2312yes—
142C24×C61—21no—
143C24×C61C2×D411yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—42no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—42no—
155#41×C61—42no—
156#41×C61—42no—
157#41×C61—41no—
158#41×C61—41no—
159#41×C61—41no—
160#41×C61—81no—
161#41×C61—81no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—22no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—41no—
169C2×Q8×C61—41no—
170C2×Q8×C61—42no—
171C2×Q8×C61C2×D411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—21no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—41no—
185C2×D4×C61—41no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—41no—
190C2×D4×C61—42no—
191C2×D4×C61C2×D411yescharacteristic
192C2×D4×C61C2×D411yescharacteristic
193C2×D4×C61C2×D412yes—
194C2×D4×C61C2411yescharacteristic
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—41no—
202C22×C4×C61—41no—
203C22×C4×C61—41no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209SD16×C61—44no—
210D8×C61—44no—
211M16×C61—22no—
212M16×C61—41no—
213C2×C8×C61—41no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—41no—
225C4⋊C4×C61—41no—
226C4⋊C4×C61—42no—
227C4⋊C4×C61—44no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—42no—
246C22⋊C4×C61—42no—
247C22⋊C4×C61—44no—
248C22⋊C4×C61C2×D411yescharacteristic
249C22⋊C4×C61C2×D411yescharacteristic
250C22⋊C4×C61C2×D412yes—
251C42×C61—22no—
252C42×C61—22no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—41no—
256C42×C61—41no—
257C42×C61C2×D412yes—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—22no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—81no—
265C23×C61—81no—
266C23×C61—82no—
267C23×C61#12011yescharacteristic
268C23×C61C22×D411yescharacteristic
269C23×C61C22×D411yescharacteristic
270Q8×C61—22no—
271Q8×C61—41no—
272Q8×C61—41no—
273Q8×C61—41no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61—41no—
277Q8×C61—81no—
278Q8×C61—82no—
279D4×C61—22no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—42no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—42no—
287D4×C61—42no—
288D4×C61—42no—
289D4×C61—42no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—81no—
294D4×C61—82no—
295D4×C61—82no—
296D4×C61—82no—
297D4×C61—81no—
298D4×C61—82no—
299D4×C61—84no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—81no—
326C2×C4×C61—82no—
327C2×C4×C61—82no—
328C2×C4×C61#12011yescharacteristic
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C8×C61—42no—
333#33556C6111yesmaximal, characteristic, direct product factor, Sylow
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—42no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—42no—
348C22×C61—82no—
349C22×C61—82no—
350C22×C61—81no—
351C22×C61—161no—
352C22×C61—162no—
353C22×C61C2×#12011yescharacteristic
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—21no—
357C4×C61—41no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61—41no—
361C4×C61—42no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—82no—
365C4×C61—82no—
366C4×C61B(4,𝔽2)11yescharacteristic
367C4×C61B(4,𝔽2)11yescharacteristic
368#3540C2×C6111yescharacteristic, complemented
369#3028C2×C6111yescharacteristic, complemented
370#3025C2×C6111yescharacteristic, complemented
371#3021C2×C6111yescharacteristic, complemented
372#2200C2×C6114yescomplemented
373#2198C2×C6114yescomplemented
374#2128C2×C6111yescharacteristic, complemented
375#2123C2×C6111yescharacteristic, complemented
376#2120C2×C6111yescharacteristic, complemented
377C2×C61—21no—
378C2×C61—41no—
379C2×C61—41no—
380C2×C61—41no—
381C2×C61—81no—
382C2×C61—82no—
383C2×C61—82no—
384C2×C61C2×B(4,𝔽2)11yescharacteristic
385#585C22×C6111yescharacteristic
386C2×AGL(1,ℤ/8)—21no—
387H(3,𝔽4)—21no—
388#560C22×C6112yescomplemented
389#559C22×C6112yescomplemented
390#556—21no—
391#555—21no—
392#551—21no—
393#548—21no—
394#546—21no—
395#542—22no—
396#542—21no—
397#538—22no—
398#536—21no—
399#536C22×C6111yescharacteristic
400#535C22×C6111yescharacteristic
401#525—21no—
402#525—21no—
403#525C22×C6111yescharacteristic
404#458—21no—
405#458—22no—
406#458C22×C6112yescomplemented
407#458C22×C6114yescomplemented
408B(4,𝔽2)—21no—
409B(4,𝔽2)C22×C6112yescomplemented
410#454—22no—
411#453C22×C6114yes—
412#421—21no—
413#413C22×C6111yescharacteristic
414#410—21no—
415#410—21no—
416#410C22×C6111yescharacteristic
417#410C22×C6111yescharacteristic
418#353C22×C6114yescomplemented
419#352C22×C6112yescomplemented
420#352C22×C6114yescomplemented
421AΣL(1,𝔽16)C22×C6112yescomplemented
422C61#3355611yescharacteristic, direct product factor, Sylow
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C6112yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C6111yescharacteristic
435C22×Q8D4×C6111yescharacteristic, complemented
436C22×D4D4×C6111yescharacteristic, complemented
437C23×C4D4×C6111yescharacteristic
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—42no—
440C2×SD16—41no—
441C2×D8—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—41no—
446#127C23×C6112yes—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—22no—
453#124—22no—
454#124—21no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124D4×C6112yescomplemented
459#123—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—24no—
464#123D4×C6111yescharacteristic
465#123D4×C6112yescomplemented
466#123C23×C6111yescharacteristic
467#123C23×C6112yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—21no—
487#120—21no—
488#120—22no—
489#120D4×C6111yescharacteristic
490#120C23×C6111yescharacteristic
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C6111yescharacteristic
505#117D4×C6111yescharacteristic, complemented
506#117D4×C6111yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C6112yes—
511#99—21no—
512#99—21no—
513#99—22no—
514#99—22no—
515#99—24no—
516#99C23×C6112yes—
517#99C23×C6112yes—
518C24—21no—
519C24C2×D4×C6111yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C6111yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C6111yescharacteristic
568C2×D4C2×D4×C6111yescharacteristic
569C2×D4C2×D4×C6112yes—
570C2×D4C24×C6111yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C6111yescharacteristic
581C22×C4C2×D4×C6111yescharacteristic
582C22×C4C2×D4×C6111yescharacteristic
583C22×C4C2×D4×C6111yescharacteristic
584C22×C4C2×D4×C6112yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C6111yescharacteristic
625C22⋊C4C2×D4×C6111yescharacteristic
626C22⋊C4C2×D4×C6112yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C6112yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23#120×C6111yescharacteristic
644C23C22×D4×C6111yescharacteristic
645C23C22×D4×C6111yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—82no—
672D4—82no—
673D4—81no—
674D4—82no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C6111yescharacteristic
705C2×C4#120×C6111yescharacteristic
706C2×C4#120×C6111yescharacteristic
707C2×C4C22×D4×C6111yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×#120×C6111yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C61×B(4,𝔽2)11yescharacteristic
742C4C61×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×C61×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C61C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C61
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×#41×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C61×#3540C2semidirect
2. C61×#3028C2semidirect
3. C61×#3025C2semidirect
4. C61×#3021C2semidirect
5. C61×#2200C2semidirect
6. C61×#2198C2semidirect
7. C61×#2128C2semidirect
8. C61×#2123C2semidirect
9. C61×#2120C2semidirect
13. C61×#560C22semidirect
14. C61×#559C22semidirect
31. C61×#458C22semidirect
32. C61×#458C22semidirect
34. C61×B(4,𝔽2)C22semidirect
43. C61×#353C22semidirect
44. C61×#352C22semidirect
45. C61×#352C22semidirect
46. C61×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C61D4semidirect
60. C22×D4×C61D4semidirect
82. #124×C61D4semidirect
89. #123×C61D4semidirect
129. #117×C61D4semidirect
130. #117×C61D4semidirect
333. #33556C61direct (N × H)
368. #3540C2×C61semidirect
369. #3028C2×C61semidirect
370. #3025C2×C61semidirect
371. #3021C2×C61semidirect
372. #2200C2×C61semidirect
373. #2198C2×C61semidirect
374. #2128C2×C61semidirect
375. #2123C2×C61semidirect
376. #2120C2×C61semidirect
388. #560C22×C61semidirect
389. #559C22×C61semidirect
406. #458C22×C61semidirect
407. #458C22×C61semidirect
409. B(4,𝔽2)C22×C61semidirect
418. #353C22×C61semidirect
419. #352C22×C61semidirect
420. #352C22×C61semidirect
421. AΣL(1,𝔽16)C22×C61semidirect
422. C61#33556direct (N × H)
435. C22×Q8D4×C61semidirect
436. C22×D4D4×C61semidirect
458. #124D4×C61semidirect
465. #123D4×C61semidirect
505. #117D4×C61semidirect
506. #117D4×C61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C61×#35402
C61×#30282
C61×#30252
C61×#30212
C61×#22002
C61×#21982
C61×#21282
C61×#21232
C61×#21202
#3355661